MEDIATE INFERENCE. THE SYLLOGISM.
=1. INFERENCE AND REASONING.=
Inference has been defined as both a product and a process. When
used to indicate a process the term inference becomes synonomous with
reasoning. If logicians could agree to confine inference to the product
and reasoning to the process, it would remove an ambiguity which is
more or less misleading. But since this has not become the custom, we
shall use inference as indicating the process as well as the product.
_Definitions――Middle Term Explained._
Inference is the thought process of deriving a judgment from one or two
antecedent judgments.
_Mediate inference is inference by means of a middle term._
Reasoning of this nature involves three terms, two of which are
compared with a third or middle term, and then related to each other
to form a new judgment. The middle term is the common unit, or the
_standard_ by which the other terms are measured. To illustrate: If
John and James are each six feet tall, then plainly, they are of the
same height. The standard, or _middle_ term, is “_six feet tall_.”
=2. THE SYLLOGISM.=
Just as the judgment is expressed by means of the proposition, so
mediate inference is best expressed by means of the syllogism.[9] The
following are syllogisms:
(1) James is six feet tall,
John is six feet tall,
Hence James is as tall as John.
(2) All true teachers are just,
You are a true teacher,
Hence you are just.
(3) All men are mortal,
You are a man,
Hence you are mortal.
=3. THE RULES OF THE SYLLOGISM.=
All syllogistic reasoning is conditioned by the following eight rules:
(1) A syllogism must have three, and only three, different terms.
(2) A syllogism must have three, and only three, propositions.
(3) The middle term must be distributed at least once.
(4) No term must be distributed in the conclusion which is not also
distributed in a premise.
(5) No conclusion can be drawn from two negative premises.
(6) If one premise be negative, the conclusion must be negative; and
conversely, to prove a negative conclusion, one of the premises
must be negative.
(7) No conclusion can be drawn from two particular premises.
(8) If one premise be particular, the conclusion must be particular.
These rules are exceedingly important, as their observance is necessary
in all mediate reasoning. The student needs, not only to understand
the meaning of these rules, but he needs to commit them to memory so
thoroughly that they may be recalled without hesitation or mistake. To
aid the memory, the eight rules may be divided into these four groups:
I. Rules one and two relate to the _composition of the syllogism_.
II. Rules three and four pertain to the _distribution of terms_.
III. Rules five and six have reference to _negative premises_.
IV. Rules seven and eight concern _particular premises_.
=4. RULES OF THE SYLLOGISM EXPLAINED.=
(1) _A syllogism must have three and only three terms._
It is common to represent the various syllogistic forms by symbols,
the same symbols always standing for the same terms. In this treatment
we shall let capital G stand for the major term, as “major” means
_greater_; capital S for the minor term, as “minor” means _smaller_,
and capital M for the middle term. G, S and M, the initial letters
of greater (major), smaller (minor) and middle, will be the constant
symbols for these terms; just as A, E, I and O are used as the constant
symbols for the four logical propositions.
_Illustration._
Syllogism written in full:
All men are mortal,
Socrates is a man,
――――――――――――――――――
(Therefore) Socrates is mortal.
Syllogism symbolized:
All M is G
S is M
――――――
∴ S is G
_The major term is always the predicate and the minor term the
subject of the conclusion._ The conclusion of the foregoing syllogism
is, “Socrates is mortal.” Since G stands for the predicate of every
conclusion, then it stands for “_mortal_,” the predicate of the above
conclusion. For a similar reason, S stands for the subject, namely,
“_Socrates_”; while M represents the middle term, “_man_.”
Since every syllogism must have three propositions, and since it takes
two terms to form a proposition, then it follows that every syllogism
must contain _six terms_. But, as no syllogism can have _more_ than
three _different_ terms, we conclude that each term of the syllogism
must be used _twice_. In the foregoing example, G thus appears,
not only in the last proposition, or conclusion, but in the first
proposition also. Similarly, both S and M occur twice. Every logical
syllogism, then, contains first, _a major term_, which is always the
_predicate_ of the conclusion and appears _once_ in the premises;
second, a _minor term_, which is always the _subject_ of the conclusion
and appears _once_ in the premises; and third, a _middle term_ to which
the other two terms are referred.
There are two ways of locating the middle term; first, it is the term
which is used in _both_ the premises; second, it is the term which
_never appears in the conclusion_. Likewise, there are two ways of
locating the major and minor terms; first, the major term is always
the _predicate_ and the minor term the _subject_ of the conclusion;
second, the major term is usually the _broader_ and the minor term the
_narrower_ of the two. If the major and minor terms seem to be of about
the same extension or breadth, then the term in the first proposition,
which is not the middle term, is the major.
In the attending syllogisms the three terms are designated:
(middle) (major)
| |
(1) All true teachers are sympathetic,
(minor) (middle)
| |
You are a true teacher,
(minor) (major)
| |
∴ You are sympathetic.
(major) (middle)
| |
(2) No shell fish are vertebrates,
(minor) (middle)
| |
All trout are vertebrates,
(minor) (major)
| |
∴ No trout are shell fish.
The necessity of having but _three_ different terms in any syllogism
may be understood by supposing that there are four different terms;
then it would follow that there could be _no standard_ or common link.
In the axiom, “Things equal to the same thing are equal to each other,”
the _same thing_ is the common standard or link. Two things which equal
two different things are not equal to each other.
The impossibility of reasoning from four terms may be shown by circles.
All men are mortal.
All trees grow.
Illustration: FIG. 8.
These circles show that no connection can be established between either
group. Using four terms in any syllogism is known as the _fallacy of
four terms_.
(2) _A syllogism must have three and only three propositions._ The
proposition containing the major term is called the _major premise_,
while the one containing the minor term is called the _minor premise_.
In a strictly logical syllogism the major premise is written first,
the minor premise second and the conclusion third. In common parlance,
however, the minor premise or even the conclusion may appear first.
The conclusion of a syllogism is always preceded by _therefore_, or
its equivalent, which may be written or understood. The premises always
answer the question, Why is the conclusion true? The premises are often
preceded by such words as _for_ and _because_.
The attending irregular syllogisms are arranged logically and the
premises and conclusions indicated:
(1a) _Illogical._
“You must take an examination because all who enter the school are
examined and you, as I understand it, are planning to enter.”
(2a) “Some of these books are not well bound, for they are going to
pieces as no well bound book would do.”
(1b) _Logical._
All who enter this school are examined, Major premise.
You are planning to enter this school, Minor premise.
You must be examined. Conclusion.
(2b)
No well bound book goes to pieces, Major premise.
Some of these books are going to pieces, Minor premise.
Some of these books are not well bound. Conclusion.
The fact that all syllogisms must have three and only three premises
follows from rule “1.” One premise must compare the middle term with
the “major”; another premise must compare the middle term with the
“minor”; while the conclusion links together the “major” and the
“minor.”
(3) _The middle term must be distributed at least once._ The rule is
usually given in this way, “The middle term must be distributed once at
least, and must not be ambiguous.” In this treatment the last part of
the rule has been omitted because it must be apparent to the student
that a middle term used in two senses is virtually equivalent to _two
different terms_; such an “ambiguous middle” would, in consequence,
give a syllogism of _four terms_.
Rules 3 and 4 are of greater importance than the others because they
are more frequently violated. If the middle term is not distributed
at least once, the fallacy is referred to as “_undistributed middle_.”
If the distributed major term of the conclusion is not distributed
in the major premise, then the fallacy is called, “_illicit process
of the major term_”; and finally, if the distributed minor term of
the conclusion is not distributed in the minor premise the fallacy is
denominated an “_illicit process of the minor term_.” These two illicit
processes may be abbreviated to illicit major and illicit minor.
Recall that any term is distributed when it is referred to as a
definite whole. Unless the whole of the middle term is considered it
fails to become a common standard of comparison. This becomes clear
when recourse is made to the circles.
_Illustration._
Syllogism in which the middle term is not distributed:
All men are mortal,
All trees are mortal,
∴ All trees are men.
All the propositions are A’s and consequently the predicates of each
are undistributed, as A distributes the subject _only_. Therefore the
middle term, “_mortal_,” is not distributed in either of the premises
and thus the fallacy.
Fallacy shown by circles:
Illustration: FIG. 9.
These circles indicate the correct meaning of the two premises. By them
it is seen that all of the “men” circle belongs to the “mortal” circle
and all of the “tree” circle belongs to the “mortal” circle, but in
this case there is no connection between the “men” and “tree” circles.
Thus, to say that “_All trees are men_,” is fallacious. We have no
right to either affirm or deny the connection between men and trees.
If “mortal” were distributed we would have this right as the following
will make clear:
All men are mortal,
No stones are mortal,
∴ No stones are men.
Illustration: FIG. 10.
Here the middle term _mortal_ is distributed in the second premise
as in it the subject “_stones_” is _excluded_ from the entire mortal
territory. This conclusion is verified by the formal statement that “E”
distributes both subject and predicate. Since all of the “men” circle
belongs to the “mortal” circle and none of the “stones” circle belongs
to the “mortal” circle then none of the “stones” circle can belong to
the “men” circle.
(4) _No term must be distributed in the conclusion which is not also
distributed in its premise._
It has been affirmed that a term is distributed when it is referred to
as a definite whole. To put it in another way, a term is distributed
when it is employed in its fullest sense. It is obvious that we should
not employ a term in its fullest sense in the conclusion when it has
been used only in a partial sense in its premise. What is said of the
part cannot necessarily be said of the whole. For example: Because
_some_ men are honest it does not follow that _all_ men are honest. Of
course the converse of this is true, namely, if it could be proved that
all men are honest then surely it would follow that some of the men are
honest. To put it briefly: What is true of _all_ is true of _some_ but
what is true of _some_ is not necessarily true of _all_.
To distribute a term in the conclusion when it is not distributed in
the premise where it occurs is equivalent to saying, “what is true of
some is true of all.” This error which violates rule “4” leads to the
two fallacies of illicit process of the major and minor terms. The
following illustrate the two fallacies.
Syllogism illustrating illicit major:
All trees grow,
No men are trees,
∴ No men grow.
The first premise is an A and consequently its subject is distributed.
The second premise and conclusion being E’s have both subject and
predicate distributed. Thus _grow_, as used in the conclusion, is
distributed, but, as used in the major premise, it is not distributed.
Fallacy shown by circles:
Illustration: FIG. 11.
Here all of the “tree” circle belongs to the “grow” circle and none
of the “men” circle belongs to the “tree” circle, hence the diagram
correctly represents the meaning of the two premises and shows the
fallacy of concluding that _no men grow_. The “men” circle, being
entirely within the “grow” circle, indicates that _all men grow_.
Syllogism illustrating illicit minor:
All true teachers are just,
All true teachers are sympathetic,
∴ All the sympathetic are just.
Each proposition being an A distributes its subject. But the subject of
the conclusion which is “_the sympathetic_” is not distributed in the
minor premise, as an A proposition distributes its subject only. Hence
the fallacy of illicit minor.
Fallacy shown by circles:
Illustration: FIG. 12.
The diagram correctly represents the two premises since all of the
“true teacher” circle belongs to both the “just” and “sympathetic”
circles. But all of the “sympathetic” circle does not belong to the
“just” circle. Hence the fallacy.
(5) _No conclusion can be drawn from two negative premises._
When two terms are both denied of a third term, it is quite impossible
to draw any conclusion relative to the two terms, as the absolute
exclusion of the third term eliminates any possibility of a common link
or standard.
The circles will make this apparent:
No men are immortal,
No trees are immortal,
Illustration: FIG. 13.
“No trees are men” is the conclusion represented by Fig. 13.
Other possible conclusions are, “_All trees are men_,” “_All men are
trees_” and “_Some men are trees_.”
It is thus seen that no definite conclusion can be drawn. It may now
be said that when the major and minor terms are used in two negative
premises the connection between them is _indeterminate_. This violation
of rule “5” may be termed the fallacy of _two negatives_.
(6) _If one premise be negative the conclusion must be negative; and
conversely, to prove a negative conclusion one of the premises must be
negative._
Referring to the first part of this rule, it may be said of two terms
that if one is affirmed and the other denied of a third term, then the
two terms must be denied of each other. The attending syllogism and its
“circled” representation will throw light upon this:
No men are immortal,
All Americans are men,
∴ No Americans are immortal.
Illustration: FIG. 14.
Since none of the “men” circle belongs to the “immortal” circle and all
of the “American” circle is inside the “men” circle, it is evident that
none of the “American” circle can belong to any part of the “immortal”
circle. Thus it is manifest that an affirmative conclusion like, “All
Americans are immortal,” is invalid.
The converse of rule 6, “To prove a negative conclusion, one of the
premises must be negative,” may be explained by the general principle
in logic that when two terms are known to disagree, one must agree with
a third term while the other must disagree. If both agreed with a third,
then the conclusion would of necessity be affirmative. If both
disagreed no conclusion could be drawn. A violation of rule 6 may be
called the fallacy of _negative conclusion_.
(7) _No conclusion can be drawn from two particular premises._ Proof:
(1) All the possible combinations of the two particular premises
I and O are, (1) IO, (2) OI, (3) II, (4) OO.
“IO” considered.
(2) Since O is a negative premise the conclusion would have to be
negative according to rule 6. (If one premise is negative, the
conclusion must be negative.)
(3) If the conclusion is negative, then its predicate, which is
the major term, must be distributed. (All negative propositions
distribute their predicates.)
(4) If the major term is distributed in the conclusion, it must
be distributed in the major premise, rule 4. (No term must be
distributed in the conclusion, which is not also distributed in
one of the premises.)
(5) Hence two terms must be distributed in the premises, the major
term according to (4) and the middle term according to rule 3.
(6) But I distributes neither term and O distributes its predicate
only; I and O together, then, distribute but _one_ term.
(7) To draw a negative conclusion the premises must distribute two
terms, the middle and the major, according to the foregoing.
(8) Hence a conclusion from I and O is untenable. The same may be
said of “OI.”
“II” considered.
(1) The I proposition distributes neither subject nor predicate,
hence the premises “II” would distribute no term.
(2) But the middle term must be distributed at least once according
to rule 3.
(3) Therefore no conclusion can be drawn from “II.”
A valid conclusion from “OO” is impossible according to rule 5.
(8) _If one premise be particular the conclusion must be particular._
Proof: The possible combinations conditioned by rule 8 are AI, AO, EI,
EO, IO, II, OO.
“AI” considered.
(1) Proposition A distributes its subject, proposition I neither;
hence “AI” together distribute but one term.
(2) According to rule 3 this one term must be the middle term.
(3) The minor term must, therefore, be undistributed in the minor
premise, and in consequence undistributed in the conclusion.
(4) But this undistributed minor term is the subject of the
conclusion; hence said conclusion must be particular, as only
particulars have an undistributed subject.
“AO” and “EI” considered.
Proof:
(1) “AO” distribute two terms; so do “EI.”
(2) Both “AO” and “EI” must have negative conclusions according to
rule 6.
(3) A negative conclusion distributes its predicate which is the
major term.
(4) The major term and the middle term must be distributed in the
premises. Rules 4 and 3.
(5) Thus the third term, which is the minor, cannot be distributed
in the minor premise and, consequently, the minor cannot be
distributed in the conclusion.
(6) This necessitates a particular conclusion.
Premises EO and OO, being negative, cannot yield a conclusion according
to rule 5; similarly, neither can the particulars IO and II because of
rule 7.
=5. THE DICTUM OF ARISTOTLE.=
Aristotle gives an axiom on which all syllogistic inference is
based. Indeed from this fundamental principle the significant rules
of the syllogism could be derived. The dictum is stated in this wise:
“Whatever is predicated, whether affirmatively or negatively, of
a term distributed may be predicated in the manner of everything
contained under it.” The following statements represent various ways
of explaining this dictum:
(1) Whatever is said of a term used in its fullest sense may likewise
be said of that term when used only in a partial sense.
(2) What is true of the whole is true of the part.
(3) “What pertains to the higher class pertains also to the lower.”
Since this dictum is the basic principle underlying the important
rules of the syllogism, it is unnecessary to dwell longer
upon it; because an explanation of the rules is, virtually, an
explanation of the dictum.
=6. CANONS OF THE SYLLOGISM.=
The dictum of Aristotle is ostensibly a self-evident truth, and some
logicians have put this truth in the form of three axiomatic statements
which are known as the _canons of the syllogism_. These are as follows:
(1) “Two terms agreeing with one and the same third term agree with
each other.”
(2) “Two terms of which one agrees and the other does not agree with
one and the same third term, do not agree with each other.”
(3) “Two terms both disagreeing with one and the same third term may
or may not agree with each other.”
Making use of the symbols as explained on a previous page of this
chapter, it will be seen that the first canon conforms to this
syllogistic type:
All M is G
All S is M
――――――――――
∴ All S is G
The two terms are S and G, while M is the third term.
The attending symbolizations illustrate, respectively, the second and
third canons:
No M is G
All S is M
――――――――――
∴ No S is G
No M is G
No S is M
Conclusion indeterminate.
=7. THREE MATHEMATICAL AXIOMS.=
Analogous to the three canons treated in “6,” there are certain
mathematical axioms which are here stated:
(1) “Things equal to the same thing are equal to each other.”
(2) “One thing equal to and the other thing not equal to the same
third thing are not equal to each other.”
(3) “Things not equal to the same thing may or may not equal each
other.”
Illustrations of the three axioms:
(1) If x equals 5, and y equals 5, then x equals y.
(2) If x equals 5, and y does not equal 5, then x does not equal y.
(3) If x does not equal 5, and y does not equal 5, then x may or may
not equal y.
=8. OUTLINE.=
MEDIATE INFERENCE.
(1) Inference and reasoning.
Definitions. Middle term explained.
(2) The analogy between the judgment and the syllogism.
(3) Rules of the syllogism given. Eight in number.
(4) Rules of the syllogism explained:
Rule 1. Syllogistic symbols.
Major, minor, and middle terms; how found.
Fallacy of four terms.
Rule 2. Major and minor premises and conclusion, how determined.
Logical arrangement.
Reason for three propositions.
Rule 3. Reason for omitting “ambiguous middle” from rule.
Undistributed and distributed middle explained.
Rule 4. Illicit major and minor explained and illustrated.
Rule 5. Fallacy of two negatives.
Rule 6. Fallacy of negative conclusion.
Rule 7. Fallacy of two particulars.
Rule 8. Fallacy of particular conclusion.
(5) Aristotle’s dictum.
(6) Canons of the syllogism.
(7) Mathematical axioms.
=9. SUMMARY.=
(1) Inference is a term used to denote a process as well as a product.
As a process reasoning and inference are in reality synonomous terms.
Inference is a thought process of deriving a judgment from one or two
antecedent judgments.
Mediate inference is inference by means of a middle term. Mediate
inference makes use of three terms, two of which are compared with a
third term as a standard. This third term is called the middle term.
(2) The syllogism is the common mode of expression for mediate
inference.
(3) Valid syllogistic reasoning is conditioned by eight rules. The
first and second relate to the composition of the syllogism; the
third and fourth to the distribution of terms; the fifth and sixth
to negative premises; the seventh and eighth to particular premises.
(4) All syllogisms must have three terms: the major, the minor, and the
middle. The middle term occurs twice in the premises but never appears
in the conclusion. The minor term is always the subject, and the major
term the predicate of the conclusion. The major term is usually broader
than the minor.
No conclusion can be drawn from four terms. To attempt this gives rise
to the fallacy of four terms.
All syllogisms must have three propositions, the major and the
minor premises, and the conclusion. The major premise first and the
minor second is the more logical arrangement, although the common
conversational form is to use the minor premise first.
Ambiguous middle amounts to the fallacy of four terms.
Unless the middle term is distributed at least once in the syllogism,
it fails to become a common standard.
Distributing a term in the conclusion, without its being distributed in
its premise, is equivalent to asserting that, “What is true of a part
is true of the whole.” This error results in the fallacies of illicit
major and minor.
A conclusion from two negatives is impossible, because of the total
exclusion of the middle term.
Of two terms, if one is affirmed and the other denied of a third term,
then they must be denied of each other; and, conversely, if two terms
are to be denied of each other, one must be affirmed and the other
denied of a given third term. This fundamental principle necessitates
deriving a negative conclusion from two premises when one is negative.
It, likewise, compels the converse of this.
A valid conclusion from two particulars is untenable because of the
two negative fallacies, or some fallacy relative to the distribution
of terms.
One particular premise forces a particular conclusion because of the
fallacies of two negatives, two particulars, and illicit minor.
(5) Aristotle’s dictum simplified means, “What is true of the whole is
true of the part.”
(6) The canons of the syllogism, three in number, are:
(1) “Two terms agreeing with one and the same third term agree with
each other.”
(2) “Two terms of which one agrees and the other does not agree with
one and the same third term do not agree with each other.”
(3) “Two terms both disagreeing with one and the same third term may
or may not agree with each other.”
(7) The foregoing canons may be stated as mathematical axioms.
=10. ILLUSTRATIVE EXERCISES.=
(1a) Make use of the proper symbols and indicate the three terms of
each of the attending syllogisms:
(1) All fixed stars twinkle,
Vega is a fixed star,
――――――――――――――――――――――――
∴ Vega twinkles.
(2) All men are rational beings,
No tree is a rational being,
――――――――――――――――――――――――――――
∴ No trees are men.
(3) All good citizens are law abiding,
All good citizens vote,
――――――――――――――――――――――――――――――――――
∴ Some who vote are law abiding.
I recall that the three terms are the middle, the major and the minor,
and that the “middle” does not occur in the conclusion, whereas the
“major” is always the predicate and the “minor” the subject of the
conclusion. The symbols M, G and S being the initial letters of middle,
greater and smaller, I make use of these in designating the three terms,
as the following will illustrate:
M G
(1) All fixed stars twinkle,
S M
Vega is a fixed star,
――――――――――――――――――――――――
S G
∴ Vega twinkles.
“Twinkles” being the predicate of the conclusion is designated as being
the major term by putting the letter G above it. Then “G” is placed
above the term “twinkle” in the first premise.
“S” is placed above the subject of the conclusion to indicate that it
is the minor term. “S” is also placed above “Vega,” the minor term, as
found in the second premise.
The remaining term, “fixed stars,” must be the middle term, therefore
I place “M” above it. The fact that “fixed star” does not occur in the
conclusion verifies this.
Using only the symbols, the syllogism takes this form:
All M is G
S is M
――――――
∴ S is G
Using the symbols to represent the other syllogisms, we have
(2) All G is M
No S is M
―――――――――
∴ No S is G
(3) All M is G
All M is S
――――――
∴ Some S is G
(1b) Indicate by symbols the three terms of the following syllogisms:
(1) No trees are men,
All rational beings are men,
――――――――――――――――――――――――――――
∴ No rational being is a tree.
(2) All men have the power of speech,
You are a man,
―――――――――――――――――――――――――――――――――
∴ You have the power of speech.
(3) Some men are wise,
All men are rational,
―――――――――――――――――――――
∴ Some rational beings are wise.
(2a) Illustrate by syllogism the fallacy of undistributed middle. An
easy way is to use _the middle term as the predicate of two A premises_.
This yields the fallacy because an A proposition does not distribute
the predicate.
The illustration: distributed terms underscored.
All true teachers are students,
―――――――――――――
All scholars are students,
――――――――
――――――――――――――――――――――――――――――――
∴ All scholars are true teachers.
――――――――
(2b) Give two illustrations of undistributed middle.
(3a) Give syllogistic illustrations of the fallacies of illicit major
and minor.
_Illicit Major._
_Use the middle term as the subject of an A proposition, and then as
the predicate of an E proposition._ This would necessitate a negative
conclusion in which the major term is distributed. But the major term
is not distributed in the major premise, hence the fallacy.
Illustration in which the distributed terms are underscored:
All men are mortal,
―――
No trees are men,
――――― ―――
―――――――――――――――――――
∴ No trees are mortal.
――――― ――――――
_Illicit Minor._
To illustrate this fallacy one may use _the middle term as the subject
of two A premises_. This would give an A conclusion in which the
subject is distributed. But this same term is not distributed in its
premise because here it is used as the predicate of an A. Illustration:
All earnest students study,
――――――――――――――――
All earnest students desire to succeed,
――――――――――――――――
―――――――――――――――――――――――――――――――――――――――
∴ All who desire to succeed study.
―――――――――――――――――――――――――
=11. REVIEW QUESTIONS.=
(1) Distinguish between inference and reasoning.
(2) Define inference. Mediate inference.
(3) Illustrate the difference between mediate and immediate
inference.
(4) Explain by illustration the use of the middle term.
(5) Exemplify the syllogism.
(6) State the rules of the syllogism.
(7) From the attending syllogisms select the three terms:
(1) All patriotic citizens vote,
You are a patriotic citizen,
∴ You should vote.
(2) No honest man would misrepresent,
(but) John Smith did misrepresent,
∴ John Smith is not honest.
(8) Symbolize the foregoing syllogisms.
(9) Illustrate by syllogisms the fallacy of four terms.
(10) Indicate by circles that a valid conclusion cannot be drawn from
four terms.
(11) Why must a syllogism have three and only three propositions?
(12) Indicate how the three propositions of an argument may be
designated. What is the logical arrangement?
(13) Show that an ambiguous middle amounts to a fallacy of four terms.
(14) Explain and illustrate undistributed middle, illicit major,
illicit minor.
(15) Exemplify the fallacies of question “14” by using circles.
(16) Explain by circles why a conclusion cannot be drawn from two
negatives.
(17) Make clear that a negative conclusion must follow, if one premise
be negative.
(18) State and explain the principle which underlies the rule, “If the
conclusion is negative one premise must be negative.”
(19) Prove by the process of elimination that no conclusion can be
drawn from two particulars.
(20) In a way similar to that of question “19” show that if one
premise be particular the conclusion must be particular.
(21) State and explain Aristotle’s dictum.
(22) State the canons of the syllogism.
(23) Symbolize and explain by circles the three canons.
(24) Illustrate the three mathematical axioms which the canons
suggest.
=12. QUESTIONS FOR ORIGINAL THOUGHT AND INVESTIGATION.=
(1) Give an illustration of a valid conclusion being drawn from four
terms.
(2) Explain by circles the foregoing.
(3) From three different business transactions, select the middle
term of comparison.
(4) Why should not those who are given to much which is argumentative,
speak in syllogistic terms?
(5) “He is a man of high ideals, and you know him to be strictly
honest, therefore you have no excuse for not voting for him.”
Recast this quotation with a view of making a logical syllogism.
(6) Show by circles that there may be a vital difference between a
_syllogism_ of three terms and an _equation_ of three terms.
(7) Indicate by illustration that in conversational argumentation the
minor premise naturally comes first.
(8) Show by circles the meaning of “indeterminate conclusion.”
(9) Rule five states that no conclusion can be drawn from two
negatives. Defend this rule in connection with the following
syllogism, which seems to contain a valid conclusion:
Any statement which is not true cannot be accepted,
This statement is not true,
∴ It cannot be accepted.
(10) If the conclusion is particular, must one premise be particular?
Explain.